Characterization of a Triplet Vinylidene

Singlet vinylidenes (R2C=C:) are proposed as intermediates in a series of organic reactions, and very few have been studied by matrix isolation or gas-phase spectroscopy. Triplet vinylidenes, however, featuring two unpaired electrons at a monosubstituted carbon atom are thus far only predicted as electronically excited-state species and represent an unexplored class of carbon-centered diradicals. We report the photochemical generation and low-temperature EPR/ENDOR characterization of the first ground-state high-spin (triplet) vinylidene. The zero-field splitting parameters (D = 0.377 cm–1 and |E|/D = 0.028) were determined, and the 13C hyperfine coupling tensor was obtained by 13C-ENDOR measurements. Most strikingly, the isotropic 13C hyperfine coupling constant (50 MHz) is far smaller than the characteristic values of triplet carbenes, demonstrating a unique electronic structure which is supported by quantum chemical calculations.


Materials and Methods (Synthesis)
All solvents were purified with a MBraun SPS -800 and additionally dried over molecular sieves and degassed with argon. Reactions were carried out either under N2 or Ar atmosphere. Solids were handled and NMR and EPR samples were prepared in a nitrogen-filled glovebox. High Under an atmosphere of argon, a solution of 1 (101 mg, 0.2 mmol, 1.0 eq.) in toluene (15 mL) at ambient temperature was irradiated with a 390 nm Kessil lamp (10 cm distance) for 1 h. A color change from orange to red-pink was observed. The solvent was removed under reduced pressure.
The resulting solid was extracted with pentane (2 x 8 mL) and the solvent removed under reduced pressure. Filtration over celite and crystallization from pentane at -40 °C furnished 3 (71 mg, 0.15 mmol, 75%) as a red-pink solid.

Geometries
All quantum chemical calculations in the present work were performed with the Orca package. 2 Geometries of vinylidene 2 and of a simplified model where all ring substituents were replaced by hydrogen atoms were optimized in both spin triplet and singlet states with the B3LYP functional. [3][4] The def2-TZVP basis sets were used on all atoms. 5 A fully decontracted version of the auxiliary def2/J basis set 6 was employed for fitting of the Coulomb integrals, while the chain-of-spheres approximation 7 was used for exact exchange. Tight convergence criteria were used both for the energy and the gradient, while significantly increased integration grids were applied throughout (Grid6 and GridX8 in Orca convention) to ensure elimination of numerical errors. Using statespecific optimized geometries of the singlet and triplet states of vinylidene 2, the triplet minimum is predicted to be 7.2 kcal/mol lower than the singlet minimum at the B3LYP/def2-TZVP level.

EPR parameters
The triplet ground state geometry was used for single-point calculations of the zero-field splitting (ZFS) parameters, i.e. the D tensor, and of 13 C hyperfine coupling constants (HFCs), i.e. the A tensors. EPR calculations were performed with the TPSSh functional, 8 which is known from extensive experience to be one of the best choices for EPR parameters, particularly for hyperfine coupling tensors of challenging systems. [9][10][11][12][13] Comparison with B3PW91, an alternative choice that performs well for HFCs in some compound classes, 14 showed negligible differences. A more important parameter concerns the choice of basis set for the calculation of hyperfine coupling constants (HFC), because of the increased requirements in the description of spin polarization and the spin density distribution close to the nucleus. For this reason the purpose-made EPR-II basis set 15 was used on selected atoms for HFC calculations, while other atoms were still described with the def2-TZVP basis set. An alternative choice of basis set optimized for the calculation of HFCs is the pcH-2 basis set by Jakobsen and Jensen. 16 We confirmed that the two basis sets agree on 13 C Aiso values within 0.5 MHz. The A tensor calculations included the isotropic (Fermi contact) and dipolar contribution for the 13 C nucleus. D tensor calculations included both spin-spin coupling (DSSC) and spin-orbit coupling (DSOC) contributions to the ZFS. The spin-spin contributions were computed on the basis of unrestricted natural orbitals (UNOs). [17][18] The spin-orbit components were derived with the coupled-perturbed approach 19 using a mean-field approximation to the Breit-Pauli operator as an effective potential spin-orbit coupling operator. [20][21][22]

Correlated wave function based calculations
Going beyond DFT, we used the domain-based local pair natural orbital implementation of coupled cluster theory with singles, doubles, and perturbative triples excitations, DLPNO-S-8 CCSD(T). [23][24][25] This method provides results that reproduce closely the results of canonical CCSD(T), which is considered the "gold standard" of modern quantum chemistry. The DLPNO-CCSD(T) approach was also used recently as the benchmark method to produce reference-quality spin-state energetics and electronic structure analysis of aryl-carbenes. [26][27][28] For the present purposes we used the "TightPNO" collective setting in Orca, the highest available default setting. In addition, we utilized the "T1" approximation for the perturbative triples component as opposed to the less reliable "T0" approach. 29 For both spin states Kohn-Sham orbitals were used as initial input for the DLPNO procedure.
Both DFT and DLPNO-CCSD(T) are single-reference approaches that compare the ground state triplet with a closed-shell excited singlet state, but by definition they cannot address the possibility of an "open-shell" singlet state. Therefore, as a final level of refinement we performed complete active space self-consistent field (CASSCF) calculations utilizing a complete active space of 10 electrons distributed within 8 valence orbitals, i.e. CAS (10,8). The capability of Orca to average over states of different spin multiplicity was leveraged to perform state-averaged orbital optimization over the lowest triplet and the two lowest singlet states simultaneously. The resulting orbitals (see Figure S6) were subsequently used in a multireference perturbation theory treatment using the N-electron valence state perturbation theory, NEVPT2, [30][31] to include dynamic electron correlation. All wave function based methods were applied on a simplified model of vinylidene 2 where the ring substituents were replaced with hydrogens. The def2-TZVP basis sets were used throughout.

Computed singlet-triplet gaps
The inherent spin-state energetics of the simplified (H-substituted) heterocyclic system of vinylidene 2 were probed at three different levels of theory. First, DFT calculations with the B3LYP functional yield a preference of 14.3 kcal/mol for the triplet state (adiabatic energy difference: 12.2 kcal/mol), compared to the lowest singlet state in which the non-bonding in-plane orbital of the monovalent carbon is unoccupied (see Figure 5). To address potential biases of DFT, at a second level of refinement we used the most accurate implementation of the domain-based local pair natural orbital implementation of coupled cluster theory with singles, doubles, and perturbative triples excitations, DLPNO-CCSD(T1). [23][24][25]29 This provides a vertical energy gap of 13.1 kcal/mol for the model system in favor of the triplet state.
Finally, we turned to multireference calculations, which allow us to also probe the "open-shell" singlet state. CASSCF and NEVPT2 place the closed-shell singlet at 12.0 kcal/mol and 12.2 kcal/mol, respectively, above the ground state triplet state. The open-shell singlet state, with the same orbital occupation as the triplet ground state, is predicted to be at 17.0 kcal/mol by CASSCF and at 13.6 kcal/mol by NEVPT2.
In conclusion, all levels of quantum chemical treatment concur that the excited singlet states, regardless of their exact electronic character, are more than 12 kcal/mol above the ground state triplet state for the simplified model of the vinylidene ( Figure S7). The exceptional agreement of the DFT values with both DLPNO-CCSD(T) and NEVPT2 results give strong confidence in the reliability of the singlet-triplet gap predicted by DFT also for the full model of vinylidene 2.

EPR sample preparation
All samples were prepared in a nitrogen-filled glovebox. For Q-band measurements a 20 ± 1 mM solution of 1 in thoroughly degassed, dry toluene was transferred into a 1.6 mm quartz tube (1.5 cm filling height), cooled to -40 °C for 15 min and sealed with Critoseal (3-5 mm). For X-band measurements a 6 ± 1 mM solution of 1 in thoroughly degassed, dry toluene was transferred into a J-Young capped 4 mm quartz tube (1.5 cm filling height) and closed at room temperature. The samples were covered in aluminum foil inside the glovebox and transported to the spectrometer under exclusion of light.

EPR experimental details
Q-Band pulse EPR measurements were carried out at 6 K using a Bruker Elexsys E580 spectrometer equipped with a 150 W TWT amplifier, Bruker EN 5107D2 resonator, Oxford Instruments CF935 continuous-flow helium cryostat and Oxford Instruments MercuryiTC temperature controller. Field-swept EPR spectra were detected via the free induction decay (FID) signal to avoid strong nuclear modulation artifacts found in the electron spin echo detected spectra. The microwave (MW) π/2 pulse was 500 ns. The triplet species was generated by irradiating the diazo precursor (20 mM) in frozen toluene solution at 10 K using a Hg arc lamp (LOT LSB610U) inside the resonator for 1 hour.
Orientation-selective Davies ENDOR spectra were collected at 6 K using an AR 600 W radiofrequency (RF) amplifier (AR 600A225A). The following microwave pulse sequence was used: π−T−π/2−τ−π−τ−echo. The RF pulse was applied during the time interval T and had a length of 30 µs; the MW inversion π pulse was 28−30 ns; the π/2 and π detection pulses were 14 and 28 ns, respectively; the inter-pulse delay τ was 340 ns.
Temperature-dependent X-band continuous wave (CW) EPR measurements were carried out in the range of 6 to 50 K using a Bruker Elexsys E500 spectrometer equipped with a Bruker ER 4116DM resonator, Oxford Instruments ESR 900 cryostat and Oxford Instruments MercuryiTC temperature controller. The spectra were recorded under non-saturating conditions, with a modulation amplitude of 7 G. The triplet species was generated by irradiating the diazo precursor (6 mM) in frozen toluene solution at 7 K using a Xe arc lamp (LOT-QuantumDesign, 300W) inside the resonator for 1 hour.
X-Band CW EPR measurements for the stability study were carried out using a Bruker Elexsys E500 spectrometer equipped with a Bruker ER 4122SHQE resonator and ER 4141VT variable temperature accessory. The spectra were recorded under non-saturating conditions (0.2 mW) in the temperature range 82 -100 K; the modulation amplitude was 15 G. The triplet species was S-11 generated by irradiating the diazo precursor (6 mM) in frozen toluene solution at 82 K using a UV diode ( = 395 nm) inside the resonator for 30 minutes.
EPR and ENDOR simulations were performed using the EasySpin package 32

Determination of the sign of D
The sign of D can be determined from the intensity difference between the MS = −1 ↔ 0 and MS = 0 ↔ 1 transitions at low temperatures. The former has a higher intensity than the latter due to the Boltzmann distribution of the electronic MS states populations (see Figure S8). In the triplet EPR spectrum of 2 recorded at 6 K, the canonical field positions X − and Y − are found on the lowfield side, indicating D > 0 (see Figure 3 and Figure S9).  Figure S9. FID-detected Q-band (fMW ≈ 33.9 GHz) EPR spectra of 2 in toluene collected at 6 K for a 13 C-labeled (red) and natural abundance (black) sample. No hf splitting is observed in the field-swept EPR spectrum upon 13 C labeling.

EPR line shape comparison for a 13 C-labeled and natural abundance sample
S-13 Figure S10. Davies ENDOR spectra of 2 recorded at canonical field positions for a 13 C-labeled (red) and a natural abundance (dark blue) sample. Subtraction results for each field position are shown in Figure 4 and Figure S11.

Subtraction of 1 H and 14 N ENDOR signals
S-14

Sign of the Az component of the 13 C hf tensor
For a standard Q-band setup with a resistive magnet, magnetic field is limited by 1450 mT. Thus, the Zcanonical field position (~1600 mT) cannot be probed experimentally. This creates an uncertainty in the experimentally determined Az component of the 13   S-15

ENDOR simulations based on the spin Hamiltonian parameters derived from DFT and the best fit to the data
The ZFS tensor (in cm -1 ) calculated by Orca in the molecular frame, where the z axis is along the C-C bond, x is perpendicular to the plane of the heterocycle and y is in the plane of the heterocycle, perpendicular to both x and z (see Figure S12) is given as Spin Hamiltonian parameters D and E (see Table 1 The hf tensor can then be transformed into the frame where the ZFS tensor is diagonal according to ̂′ = ̂ . The resulting matrix was used for the 13 C ENDOR simulations shown in Figure S13 B. Diagonalization of the ̂ matrix yields the hf eigenvalues given in Table 1: ).

S-16
The order of hf eigenvalues (and the corresponding RA columns) was chosen according to the labeling scheme used for the experimentally determined hf tensor values.
A rotation matrix from the ZFS frame to the hf frame can be constructed as RZFS → hf = RA T RD, where RD represents the rotation from the ZFS frame to the molecular frame, and RA T represents the rotation from the molecular frame to the hf frame.   Figure S13. Simulated 13 C ENDOR patterns obtained over the entire EPR envelope using spin Hamiltonian parameters derived from (A) the best fit to the experimental ENDOR data at canonical field positions and (B) DFT calculations performed using Orca (see Table 1 and the description above).